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(7x+2)(x+8)=90
We move all terms to the left:
(7x+2)(x+8)-(90)=0
We multiply parentheses ..
(+7x^2+56x+2x+16)-90=0
We get rid of parentheses
7x^2+56x+2x+16-90=0
We add all the numbers together, and all the variables
7x^2+58x-74=0
a = 7; b = 58; c = -74;
Δ = b2-4ac
Δ = 582-4·7·(-74)
Δ = 5436
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:x_{1}=\frac{-b-\sqrt{\Delta}}{2a}x_{2}=\frac{-b+\sqrt{\Delta}}{2a}
The end solution:
\sqrt{\Delta}=\sqrt{5436}=\sqrt{36*151}=\sqrt{36}*\sqrt{151}=6\sqrt{151}x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(58)-6\sqrt{151}}{2*7}=\frac{-58-6\sqrt{151}}{14}x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(58)+6\sqrt{151}}{2*7}=\frac{-58+6\sqrt{151}}{14}
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